The automorphism group of a free-by-cyclic groups in rank 2

2006/02/15 by O. Bogopolski, Oleg Bogopolski, Armando Martino +6
Computer Science · Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #math.GR #msc:20E06 #msc:20E36 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0602327

14 pages

arxiv created 2006/02/15 · arxiv updated 2009/12/01

Abstract

Let ϕ be an automorphism of a free group F_n of rank n, and let M_ϕ=F_n \rtimes_ϕ ℤ be the corresponding mapping torus of ϕ. We study the group Out(M_ϕ) under certain technical conditions on ϕ. Moreover, in the case of rank 2, we classify the cases when this group is finite or virtually cyclic, depending on the conjugacy class of the image of ϕ in GL₂(ℤ).

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